Lesson 1.3, For use with pages 14-20

1. Evaluate 2[54 (42 + 2)].

ANSWER 6

ANSWER 3

2. Evaluate when x = 3.5xx + 2

Write Expressions

Section 1.3

P. 15-20

• In this section you will learn how to translate verbal phrases into algebraic expressions.

Vocabulary

• Verbal Model

• Rate

• Unit Rate

Describes a real-world situation using words as labels and using math symbols to relate the words.

A rate is a fraction that compares two quantities of different units

5 pencils for $1.25 is a rate

When the fraction’s denominator is one, it is a unit rate. (per)

25 cents per pencil 25/1

Verbal Phrase

• Addition:• The ______ of 3 and a number n• 3 + n

• The number x _______ 10

• X + 10

Verbal Phrase

• Subtraction:• The __________ of 7 and the number n.• 7 – n• Twelve ______ than a number x.• X – 12

• Order is very important when writing a subtraction expression. Why?

Verbal Phrase

• Multiplication:• Five ______ a number y• 5y• The ________ of 2 and the number x• 2x

• The number always comes BEFORE the variable when a product is indicated.

Verbal Phrase

• Division:• The ________ of 6 and a number w• 6 / w

• Eight ________ into a number y• y / 8Order is important when writing division

expressions. Why?

EXAMPLE 1 Translate verbal phrases into expressions

Verbal Phrase Expression

a. 4 less than the quantity 6 times a number n

b. 3 times the sum of 7 and a number y

c. The difference of 22 and the square of a number m

6n – 4

3(7 + y)

22 – m2

GUIDED PRACTICE for Example 1

1. Translate the phrase “the quotient when the quantity 10 plus a number x is divided by 2” into an expression.

ANSWER

1. Expression 10 + x2

SOLUTION

Cutting A Ribbon

EXAMPLE 2 Write an expression

A piece of ribbon l feet long is cut from a ribbon 8 feet long. Write an expression for the length (in feet) of the remaining piece.

Draw a diagram and use a specific case to help you write the expression.Suppose the piece cut is 2 feet long.

Suppose the piece cut is L feet long.

The remaining piece is(8 – 2) feet long.

The remaining piece is(8 – l) feet long.

EXAMPLE 2 Write an expression

ANSWER

The expression 8 – l represents the length (in feet) of the remaining piece.

Write a verbal model.

SOLUTION

You work with 5 other people at an ice cream stand. All the workers put their tips into a jar and share the amount in the jar equally at the end of the day. Write an expression for each person’s share (in dollars) of the tips.

Tips

EXAMPLE 3 Use a verbal model to write an expression

Translate the verbal model into an algebraic expression. Let a represent the amount (in dollars) in the jar.

STEP 1

STEP 2Amount

in jarNumber

of people

a 6

EXAMPLE 3 Use a verbal model to write an expression

ANSWER

An expression that represents each person’s share (in dollars) is a

6

EXAMPLE 4 Find a unit rate

A car travels 110 miles in 2 hours. Find the unit rate.

110 miles 2 hours = 1 hour

55 miles2 hours 2

110 miles 2 =

The unit rate is 55 miles per hour, or 55 mi/h

ANSWER

• Assignment: P. 18 1-28• Most answers today will be short

answers, with little work